Wave Mechanics Question 616
Question: If $ n _{1} $ , $ n _{2} $ and $ n _{3} $ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by
Options:
A) $ \frac{1}{n}=\frac{1}{n _{1}}+\frac{1}{n _{2}}+\frac{1}{n _{3}} $
B) $ \frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n _{1}}}+\frac{1}{\sqrt{n _{2}}}+\frac{1}{\sqrt{n _{3}}} $
C) $ \sqrt{n}=\sqrt{n _{1}}+\sqrt{n _{2}}+\sqrt{n _{3}} $
D) $ n=n _{1}+n _{2}+n _{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Total length of string $ \ell ={\ell _{1}}+{\ell _{2}}+{\ell _{3}} $ (As string is divided into three segments) $ Butfrequency\propto \frac{1}{length} $
$ ,( \because f=\frac{1}{2\ell }\sqrt{\frac{T}{m}} ) $ so $ \frac{1}{n}=\frac{1}{n _{1}}+\frac{1}{n _{2}}+\frac{1}{n _{3}} $ .
BETA
